---
tag: 46JCQ6KDA4
kind: concept
name: Formalism
msc: [03A05]
sources:
  - url: https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics)
same_as:
  wikidata: Q1433067
  wikipedia: Formalism (philosophy of mathematics)
---

## Summary

Formalism is the view that mathematics is about formal systems: strings of symbols and the rules that transform them.
On this view, a theorem is a string derived from the axioms by the rules.
It need not describe any abstract objects.
David Hilbert is the name most linked with formalism, through [[Hilbert's program|P1RW6JWX73]].
It is one of the classical answers in the [[foundations of mathematics|EFFRJFW67Y]].

## Explanations

### L1 human

Think of mathematics as a game like chess, played with symbols instead of pieces.
The axioms are the starting position and the rules of inference are the legal moves.
For example, in a formal system for arithmetic the string $0 + 0 = 0$ is a theorem because a sequence of legal moves leads to it.
A strict formalist says that this is all there is to it, and that the question "is it really true?" does not arise.